L2 torsion without the determinant class condition and extended L2 cohomology

Maxim Braverman*, Alan Carey, Michael Farber, Varghese Mathai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L 2 cohomology. Under the determinant class assumption the L 2 torsions of this paper specialize to the invariants studied in our previous work [6]. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler [3] we obtain a Cheeger-Müller type theorem stating the equality between the combinatorial and the analytic L2 torsions.

Original languageEnglish
Pages (from-to)421-462
Number of pages42
JournalCommunications in Contemporary Mathematics
Volume7
Issue number4
DOIs
StatePublished - Aug 2005
Externally publishedYes

Funding

FundersFunder number
National Science FoundationDMS-0204421
Directorate for Mathematical and Physical Sciences0204421
Clay Mathematics Institute
Royal Society
Australian Research Council

    Keywords

    • Determinant class condition
    • Determinant lines
    • Extended l cohomology
    • L torsion

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